If x – 10 is a factor of x2 – 8x – 20, what is the other factor?

Answer:

(i) False

(ii) Selecting a 5 or a spade are not independent.

Step-by-step explanation:

(i)

Independent events are those events that occur at the same time, i.e. the occurrence of one event does not effects the occurrence of the other.

If A and B are independent events then: \(P(A\cap B)=P(A)\times P(B)\)

Whereas as if two events are mutually exclusive, then the probability of them both taking place at the same time is 0.

Then for events A and B: \(P(A\cap B)=0\)

Thus, the statement is False.

(ii)

In a standard deck of 52 cards there are:

Spades = 13

Diamond = 13

Heart = 13

Clubs = 13

And each of these 13 cards are:

K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2, A

If a card labelled as 5 is selected then it could also be a Spade.

And if a spade is selected then the card could be labelled as 5.

So, selecting a 5 or a spade are not independent.

The approximate area of the trapezoid is determined as  13.95 unit².

The approximate area of the trapezoid is calculated as follows;

Area = ¹/₂(b₁ + b₂)h

Where;

The y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;

y(3/2) = - (3/2)²/2 + 3/2 + 5

y(3/2) = -9/8 + 3/2 + 5

y(3/2) = 5.375

y(4) = -4²/2 + 4 + 5

y(4) = -8 + 9

y(4) = 1

h = 5.375 - 1 = 4.375

The approximate area of the trapezoid is calculated as;

Area = ¹/₂(5.375 + 1) x 4.375

Area = 13.95 unit²

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Answer:

The second answer is the correct answer and the explanation in the attachment

The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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Answer:

The answer is:

\((x+4)^2+(y-2)^2 = 4\)

Step-by-step explanation:

The equation of a circle:

\((x-h)^2+(y-k)^2=r^2\)

Since, you already have the center and the radius, use them for the equation of a circle and it will be written as:

\((x+4)^2+(y-2)^2 = 2^2\)

When putting the equation of a circle, the radius needs to be simplified by the exponent \(2\):

\((x+4)^2+(y-2)^2 = 4\)

So, you have found the equation of circle.

The other two factors of given polynomial are (x+2) and (2x-1).

A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.

Sums of terms with the pattern kxn—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5. Polynomials: An introduction Using the sum of powers in one or more variables multiplied by coefficients, a polynomial is a type of mathematical expression.

Given that x+3 is a factor of polynomial 2x³ + 9x² + 7x - 6. So that

2x³ + 9x² + 7x - 6

⇒ 2x³ + 6x² + + 3x² + 7x - 6

⇒ 2x²(x+3) + 3x² + 7x - 6

⇒ 2x²(x+3) + 3x² + 9x - 2x - 6

⇒ 2x²(x+3) + 3x(x+3) - 2(x+3)

⇒ (x+3)(2x² + 3x - 2)

⇒ (x+3)(2x² + 4x - x - 2)

⇒ (x+3)[2x(x+2) -1(x+2)]

⇒ (x+3)(x+2)(2x-1)

Hence, Factors of given expression are (x+3)(x+2)(2x-1)

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Answer:

Really hope this helps

Step-by-step explanation:

Tom= £149.40

Ben= £522.90

a)

We know that a 4-sided polygon's angles add up to 360 degrees

so to find x:

360-(69+118+84)=89 degrees

b)

For a 4-sided polygon we also know that the outside angles add up to 360 degree.

so to find p:

360-(100+62+106)=92 degrees

Hope it helps!

Answer:

The x-interceptis1 and y-intercept is-4

Answer:

x intercept: 1

y intercept: -4

Step-by-step explanation:

If you look at where the line hits the x axis, it hits it at 1. And if you look at where the line hits the y axis it hits it at -4.

Answer:

\(2903040\)

Step-by-step explanation:

Answer:

2,903,040 is correct answer

Answer:

\(\boxed{x = -7~~and~~ y =-7}\)

Step-by-step explanation:

y = 3x + 14

y = x

.

x = 3x + 14

3x - x = -14

2x = -14

\(x = \frac{-14}{2}\)

x = -7

.

y = x

y = -7

Answer:

x = 7 and y = -7

Step-by-step explanation:

use substitution method

\(2x^3+4x^2+2x\\\\GCF = 2x\\\\2x(\frac{2x^3}{2x}+\frac{4x^2}{2x}+\frac{2x}{2x})\\\\2x(x^2+2x+1)\\\\2x(x^2+2(x)(1)+1^2)\\\\2x(x+1)^2\)

Hope this helps, have a blessed and wonderful day!  

Answer:

C. 2x(x + 1)2

the next one is

Find the roots of the polynomial function f(x) = 2x3 + 4x2 + 2x ?

C. x = 0, x = –1 with multiplicity 2

Step-by-step explanation:

did review on edg2020

The age of Milkhail is 40 years .

In the question ,

it is given that

the the sum of ages of Gabrielle and Milkhail is = 95

let the age of Milkhail be "m" .

given that Gabrielle is 15 years older than Milkhail

So, the age of Gabrielle is = m + 15

the equation representing the sum of ages is given by

total age = age of Milkhail + age of Gabrielle

95 = m + m + 15

adding the like terms ,

we get

95 = 2m + 15

subtracting 15 from both the sides

2m = 95 - 15

2m = 80

dividing both sides by 2

m = 80/2

m = 40

Therefore , the age of Milkhail is 40 years .

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The percentage of widgets that will be scrapped is 1-0.9545=0.0455 or 4.55%.

Non-parametric techniques are often used when normality assumptions for parametric tests are not met, or data on the variable of interest are ordinal, non-normal, or show heteroscedasticity (unequal variances). There are several reasons why the investigator was advised to use non-parametric techniques to investigate whether there is a significant difference in male and female wages:

If the data are not normally distributed, which is frequently the case with wage data, using parametric methods might result in incorrect conclusions.If the standard deviation is not known, non-parametric methods might be preferred.There may be outliers in the data, and non-parametric methods are more robust than parametric methods in the presence of outliers.

Non-parametric methods can be used when the sample size is small. Part 2In order to solve the given problem we need to first calculate the Z scores and then look up the area under the normal distribution curve between the Z scores. Given that the mean of the distribution is 20g and the standard deviation is 1g, we can calculate the Z scores for 18g and 22g as follows:

Z1=(18-20)/1=-2

Z2=(22-20)/1=2

Using the standard normal distribution table, the area under the curve between Z=-2 and Z=2 is 0.9545. Therefore, the percentage of widgets that will be scrapped is 1-0.9545=0.0455 or 4.55%.

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Answer:

rfgcc ft v crytrcvrcvhtfvyrfftv ffg

Step-by-step explanation:

tgfgghcg gn v v

Answer:

3/8

Step-by-step explanation:

1/8 +1/4, so yes you find a common denominator, so 1/4, to get 8 as the denominator you multiply 4by2, so you multiply the top, so 1/4 would be 2/8. your final answer would be 1/8+1/4=1/8+2/8=3/8

The problem that can arise from different styles and formats of quotations in terms of measurements or units is inconsistency and confusion.

If different suppliers or vendors quote prices based on different measurement units or quantities, it can make it difficult to compare and evaluate the offers accurately. It may lead to misunderstandings, errors in pricing, and challenges in making informed purchasing decisions. When quotations are based on different measurement units or quantities, it becomes challenging to compare them directly. For example, one supplier may provide a quotation based on cubic measurements, while another supplier may quote based on kilograms or the number of containers. This inconsistency can create confusion and make it difficult to determine which quotation offers the best value or meets the requirements of the buyer.

In such cases, it is essential to establish a common basis for comparison. This may involve converting the quotations to a standardized unit or quantity that is relevant to the buyer's needs. For example, if one supplier quotes based on cubic measurements and another based on the number of containers, the buyer may need to convert both quotations to a common unit, such as the cost per container or per cubic measurement, to make a fair comparison.

Without a standardized basis for comparison, it becomes challenging to assess the true costs and benefits of different quotations. It can lead to misunderstandings, as the buyer may assume a certain quantity or unit of measurement based on their expectations or previous experiences. This can result in errors in pricing, incorrect budgeting, and potentially selecting a supplier that may not be the most cost-effective or suitable option.

To avoid these problems, clear communication and clarification of the quotation requirements are crucial. Buyers should specify the preferred measurement units or quantities and ask suppliers to provide quotations based on those specifications. This helps ensure consistency, accuracy, and enables an informed evaluation of the quotations to make an appropriate purchasing decision.

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In a strongly right-skewed data set, the median will be smaller than the mean. This implies that the majority of the data points are concentrated towards the lower end of the distribution, resulting in a longer tail on the right side.

The median represents the middle value of a data set when arranged in ascending order. Since the tail on the right side of the distribution is stretched due to the skewness, the median will be pulled towards the lower values, making it smaller than the mean.

The mean, on the other hand, takes into account the values of all data points and is influenced by extreme values. In a right-skewed distribution, the presence of a few very high values on the right side can significantly increase the mean. Therefore, the mean will be larger than the median, indicating the overall shift towards higher values caused by the skewness.

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A. (1,-3)

The price that is 3rd standard above the mean, if the mean is $10000  and the standard deviation is $500 is $18500.

Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Given:

The mean, m = $17000,

The standard deviation, σ = $500

Calculate the 3rd standard deviation as shown below,

3rd standard deviation  = mean + 3 × standard deviation

3rd standard deviation = 17000 + 3 × 500

3rd standard deviation = 17000 + 1500

3rd standard deviation = $18500

Therefore, the price that is 3rd standard above the mean, if the mean is $10000  and the standard deviation is $500 is $18500.

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Answer:

$150

Step-by-step explanation:

A garden table and a bench together will cost $600. The actual values of the garden table and the bend are not given, but we know that the cost of a garden table will cost three times more than the bench.

Let \(x\) = the cost of the bench.

Again, since the cost of the garden table is three times the cost of the bench (\(x\)), we can represent the garden table as three times \(x\) (\(3x\)). These two terms will equal $600 when added, so let's formulate an equation:

\(3x+x=600\)

Combine like terms:

\(4x=600\)

Divide both sides of the equation by the coefficient of \(x\), which is \(4\):

\(x=150\)

_

Check your work by substituting \(150\) into the original equation:

\(3(150)+(150)=600\)

\(450+150=600\)

\(600=600\)

Our answer is correct!

Therefore, approximately 65.9 square feet of paint will be needed to cover all visible surfaces of the rocket ship float.

Surface area is the measure of the total area that the surface of an object occupies. It is the sum of all the areas of the individual faces or surfaces of the object. For example, if you have a cube, the surface area would be the sum of the areas of all six faces of the cube. The surface area is usually measured in square units, such as square meters, square centimeters, or square feet, depending on the system of measurement used. Surface area is an important concept in many fields of study, including mathematics, physics, chemistry, and engineering.

by the question.

To calculate the total surface area that needs to be painted, we need to find the surface area of the cylinder and the surface area of the cone, and then add them together.

Surface area of the cylinder:

The cylinder has a radius of 1.5 feet and a height of 4 feet. The formula for the surface area of a cylinder is:

\(SA_cylinder = 2πrh + 2πr^2\)

where r is the radius and h is the height of the cylinder.

Plugging in the values, we get:

\(SA_cylinder = 2π(1.5)(4) + 2π(1.5)^2\\SA_cylinder = 12π + 4.5π\\SA_cylinder = 16.5π\)

\(SA_cylinder = 51.8 ft²\) (rounded to the nearest tenth)

Surface area of the cone:

The cone also has a radius of 1.5 feet, and a height of 2 feet. The formula for the surface area of a cone is:

\(SA_cone = πr√(r^2 + h^2)\)

Plugging in the values, we get:

\(SA_cone = π(1.5)√(1.5^2 + 2^2)\\SA_cone = π(1.5)√(2.25 + 4)\\SA_cone = π(1.5)√6.25\)

\(SA_cone = π(1.5)√(1.5^2 + 2^2)\\SA_cone = π(1.5)√(2.25 + 4)\\SA_cone = π(1.5)√6.25\) (rounded to the nearest tenth)

Total surface area:

Adding the surface area of the cylinder and the surface area of the cone, we get:

\(Total SA = SA_cylinder + SA_cone\)

Total SA ≈ 65.9 ft² (rounded to the nearest tenth)

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Rounded to the nearest tenth of a square foot, the area that needs to be painted is 76.9 square feet.

What exactly is a cylinder?

In geοmetry, a cylinder is οne οf the fundamental 3d fοrms with twο parallel circular bases at a distance.

The first step is to calculate the lateral surface area of the cylinder and cone. The lateral surface area of the cylinder is the product of the height and the circumference of the base, which is:

4 feet x 2π(1.5 feet) = 12π square feet

The lateral surface area of the cone is half the product of the slant height and the circumference of the base, which is:

1/2 x 2π(1.5 feet) x √(2^2 + 1.5^2) = 7.5π square feet

The total area to be painted is the sum of the lateral surface areas of the cylinder and cone, plus the area of the base of the cone, which is congruent to the base of the cylinder. The base has a radius of 1.5 feet, so the area of each base is:

π(1.5 feet)^2 = 2.25π square feet

The total area to be painted is:

12π + 7.5π + 2(2.25π) = 24.5π square feet

Using a calculator, this is approximately equal to 76.95 square feet.

Therefore, Rounded to the nearest tenth of a square foot, the area that needs to be painted is 76.9 square feet.

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Dodger Stadium: 37,036 more people can attend a Dodger game., Lambeau Field + Georgia Dome: 132,118 fans can be seated altogether in the two parks.

1) Dodger Stadium:

56,000 - 18,964 = 37,036 more people can attend a Dodger game.

2) Alamodome:

35,000 - 20,557 = 14,443 more people can be seated for special events.

3) Lambeau Field + Georgia Dome:

60,890 + 71,228 = 132,118 fans can be seated altogether in the two parks.

4) Arrowhead Pond + Staples Center:

17,174 + 18,118 = 35,292 fans can be held altogether in the two arenas.

5) United Center:

21,500 / 25 = 860 25-seat ticket packages could be sold for one game.

6) Comerica Park:

40,000 / 20 = 2,000 20-seat packages could be sold.

7) Fenway Park - Veterans Stadium:

62,409 - 33,871 = 28,538 more fans can attend a game in Philadelphia.

8) St. Louis Stadium:

66,000 / 8 = 8,250 ticket packages could be sold for one game.

9) Miami Dolphins stadium:

75,192 x 8 = 601,536 total fans could attend all 8 regular-season games.

10) Edison Field:

45,050 x 81 = 3,655,050 tickets could be sold for their 81 regular-season games.

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Answer:

Show that if \(f(a) = f(b) = 0\) for some \(a,\, b \in [-2,\, 2]\) where \(a \ne b\), then by Rolle's Theorem \(f^{\prime}(x) = 0\) for some \(x \in (-2,\, 2)\). However, no such \(x\) exists since \(f^{\prime}(x) < 0\) for all \(x \in (-2,\, 2)\!\).

Note that Rolle's Theorem alone does not give the exact value of the root. Neither does this theorem guarantee that a root exists in this interval.

Step-by-step explanation:

The function \(f(x) = x^{3} - 12\, x + 11\) is continuous and differentiable over \([-2,\, 2]\). By Rolle's Theorem. if \(f(a) = f(b)\) for some \(a,\, b \in [2,\, -2]\) where \(a \ne b\), then there would exist \(x \in (a,\, b)\) such that \(f^{\prime}(x) = 0\).

Assume by contradiction \(f(x)\) does have more than one roots over \([-2,\, 2]\). Let \(a\) and \(b\) be (two of the) roots, such that \(a \ne b\). Notice that \(f(a) = 0 = f(b)\) just as Rolle's Theorem requires. Thus- by Rolle's Theorem- there would exist \(x \in (a,\, b)\) such that \(f^{\prime}(x) = 0\).

However, no such \(x \in (a,\, b)\) could exist. Notice that \(f^{\prime}(x) = 3\, x^{2} - 12\), which is a parabola opening upwards. The only zeros of \(f^{\prime}(x)\) are \(x = (-2)\) and \(x = 2\).

However, neither \(x = (-2)\) nor \(x = 2\) are included in the open interval \((-2,\, 2)\). Additionally, \(a,\, b \in [-2,\, 2]\), meaning that \((a,\, b)\) is a subset of the open interval \((-2,\, 2)\). Thus, neither zero would be in the subset \((a,\, b)\). In other words, there is no \(x \in (a,\, b)\) such that \(f^{\prime}(x) = 0\). Contradiction.

Hence, \(f(x) = x^{3} - 12\, x + 11\) has at most one root over the interval \([-2,\, 2]\).

Answer:

Step-by-step explanation:

Find the amount of change in both cases and convert the change into percentage, then compare final results.

1. Riddington

Change:

Percent change:

2. Greenwick

Change:

Percent change:

As we see 50% > 40% so this proves the statement.

The df value for the t statistic computed for the corresponding hypothesis test is 38.

To calculate the degrees of freedom (df) for a t-test in an independent-measures research study, you need to know the sample size of each group.

Since the study compares two treatment conditions and uses a total of 40 participants, we need to assume that the sample size is equal in each group.

Therefore, each treatment condition has 20 participants (40 participants / 2 conditions).

The formula to calculate df for an independent t-test is:

df = (n1 + n2) - 2

where n1 and n2 are the sample sizes for each group.

Substituting the values, we get:

df = (20 + 20) - 2

df = 38

Therefore, the df value is 38

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Answer:

41 inches

Step-by-step explanation:

The formula for Area of a rectangle is ;

A = L × W

L = Length

W = Width

A rectangle has a length of 31 inches less than 3 times its width.

L = 3W - 31

If the area of the rectangle is 984 square inches, find the length of the rectangle

Hence,

984 = (3W - 31) × W

984 = 3W² - 31W

Hence

3W² - 31W - 984

3W(W - 24) + 4(W - 24) = 0

(3W + 41)(W - 24) = 0

W - 24 = 0

W = 24 inches

We have to find the Length

L = 3W - 31

L = 3(24) - 31

L = 72 - 31

L = 41 inches

The Length = 41 inches

The Length of the rectangle is 41 inches

The sample mean is (12.19 - 12.00) / 0.02 = 9.5 standard deviations from the mean of the distribution of sample means.

To find the probability that a random sample of size 36 has a mean of at least 12.19 ounces, we can use the formula for the z-score:

z = (x - μ) / (σ / sqrt(n))

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values we have:

z = (12.19 - 12.00) / (0.02 / sqrt(36)) = 4.5

Looking up the corresponding area under the normal curve using a standard normal table or calculator, we find that the probability of getting a sample mean of at least 12.19 ounces is extremely small, approximately 3.2 x 10^-6 or 0.00032%.

It does not appear that consumers are being cheated based on this information alone. The fact that a single sample had a slightly higher mean than the population mean does not necessarily indicate intentional deception or fraud. It is possible that the difference is due to chance variation in the manufacturing process or some other factor. To determine whether there is systematic underfilling of cans, more data would need to be collected and analyzed.

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